Beginner question: available space in a ware house I have a year's worth of data for the available slots in a warehouse. There is a data point for every minute of the year.


*

*timestamp

*available slots


The data seems to follow a certain pattern, namely, less space during the working hours, more space during the night and on the weekends.
My question is, can probability theory help me make predictions here?
How can I calculate the likelihood of the warehouse being empty, half full, full during a certain time_span / weekday combination. 
For instance, 


*

*how likely is it, that the warehouse will be mostly full between 10am and 11am on a regular Monday?

*how likely is it, that the warehouse will be empty on 2pm on a regular Thursday

 A: I guess there are many possible methods that you can use. My background is in machine learning so my biased answer would be: Use a Hidden Markov Model (HMM).
You need to train the HMM based on your observations (available slots) to learn the model's emission probability (B), transition probability (A) and prior probability (pi) matrices.
Once you know your model parameters, you can run the Viterbi algorithm on your time series to find the best (hidden) state sequence that fits your observations. This would in effect reveal the patterns in your data.
If I were you, I would initially start with an HMM with 2 hidden states, one corresponding to office hours and the other to out of office hours, and see what results you get.
The bible of HMMs, which every paper in the field references, is this tutorial by Rabiner. It is easy to follow and should give you an idea about how to implement it.
Many languages have HMM libraries so you don't have to code anything from scratch. Just google 'Language + Hidden Markov Model' and you will find a library or toolbox.
Hth.
